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Strength and Durability of Gears

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Free Gear Calculator

7. Strength and Durability of Gears / The tooth is the most crucial element of gears. Strength of gears depends on the breakage durability or friction durability.

Gear designers decide specifications in accordance with factors like torque, rotation and expected lifetime. In this section, we briefly introduce the bending strength and the surface durability.

Bending Strength of Spur Gears and Helical Gears JGMA401-01

As shown in the Figure.7.1, the tooth fillet breakage occurs at the root when applied force exceeds the limit. The following is the equation for bending stress :

Allowable Tangential Force

Allowable Tangential Force (7.1)
Fig.7.1 Lack of bending stress at root
Fig. 7.1 Lack of bending stress at root

Symbol Name Affected Factors and other Specifications
σFlim Allowable bending stress at rootName Material / Heat treatment
mn Normal Module Tooth size
b Face Width Gear size
YF Tooth Profile Factor Pressure angle/ Profile shift coefficient / Tooth width
Load Sharing Factor Contact ratio
Helix Angle Factor Helix angle of helical gear
KL Life Factor Expected lifetime
KFX Size Factor of Root Stress 1.00 at the moment (unknown)
KV Dynamic Load Factor Circumferential speed / Gear accuracy
KO Overload Factor Motor / Impact from load
SF Safety Factor It should be set to more than 1.2 for safety considerations

How to encourage bending strength

To encourage bending strength, values in the equation for allowable tangential force (7.1) should be set to; The value of denominator should be small & The numerator should be large

Surface Durability of Spur and Helical Gears JGMA402-01

Tooth surface durability is calculated in accordance with the contact stress, to figure out the strength against the tooth surface damage (Pitting).

The allowable tangential force Ftlim for surface durability is;
Allowable Tangential Force Surface Durability
Allowable Tangential Force (Ftlim)

Fig.7.2 Contact Stress
Fig. 7.2 Contact Stress

Symbol Name Affected Factors and other Specifications
σHlim Allowable Hertz Stress Material / Heat treatment
d01 Pitch Diameter of Pinion Pinion size (Diameter)
bH Effective Facewidth Gear size
i Gear Ratio (z2 / z1) Ratio of the number of teeth
ZH Zone Factor Helix angle / Profile shift coefficient
ZM Material Factor Material combination
Contact Ratio Factor Transverse / Overlap contact ratio
Helix Angle Factor 1.00 (Assumed)
ZHL Life Factor Expected lifetime
ZL Lubricant Factor Lubricants and Viscosity
ZR Surface Roughness Factor Surface roughness
ZV Lubrication Speed Factor Circumferential speed / Surface hardness
ZW Hardness Ratio Factor Hardness of wheels
KHX Size Factor 1.00 assumed
KHβ Longitudinal Load Distribution Factor Gear Support / Stiffness etc.
KV Dynamic Load Factor Circumferential speed / Gear accuracy
K0 Overload Factor Motor / Impact from load
SH Safety Factor Set to more than 1.15 for safety considerations

How to increase surface durability

The strength calculator on KHK web site

The calculation of gear strength tends to be rather complicated. On our web site, we offer a strength calculator for KHK stock gears, which enables you to calculate gear strength automatically, by inputting values in accordance with your usage condition. For gear strength calculation, there are several formulas. The gear strength formula used in our calculator is based on JGMA (Japanese Gear Manufacturers Association) specifications.

Related links :
Know about gear transmission torque
Gear Strength and Gear Durability
Bending Strength of Spur and Helical Gears
Surface Durability of Spur and Helical Gears
Bending Strength of Bevel Gears
Surface Durability of Bevel Gear
Surface Durability of Worm Gear

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